TS EAMCET 2023 (Online) 14th May Evening Shift | Three Dimensional Geometry Question 40 | Mathematics

If the foot of the perpendicular drawn from the point $(1,0,-2)$ to the plane $\pi$ is $(2,0,-1)$ and the equation of the plane $\pi$ is $a x+b y+c z=2$, then $a^2+b^2+c^2=$

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

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If $A(1,2,3), B(3,7,-2), C(6,7,7)$ and $D(-1,0,-1)$ are points in a plane, then the vector equation of the line passing through the centroids of $\triangle A B D$ and $\triangle A C D$ is

$\mathbf{r}=(2 \hat{\mathbf{i}}-\hat{\mathbf{j}})+t(\hat{\mathbf{j}}+4 \hat{\mathbf{k}})$

$\mathbf{r}=(1+t) \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 t \hat{\mathbf{k}}$

$\mathbf{r}=(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+t(\hat{\mathbf{i}}+3 \hat{\mathbf{j}})$

$\mathbf{r}=(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})+t(2 \hat{\mathbf{i}}-\hat{\mathbf{j}})$

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

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In a $\triangle A B C$, if the mid-points of sides $A B, B C$ and $C A$ are $(3,0,0),(0,4,0)$ and $(0,0,5)$ respectively, then $A B^2+B C^2+C A^2=$

200

300

400

TS EAMCET 2023 (Online) 14th May Morning Shift

MCQ (Single Correct Answer)

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If $l, m, n$ and $a, b, c$ are direction cosines of two lines, then

they are parallel when $l a+m b+n c=0$

they are perpendicular when $\frac{1}{a}=\frac{m}{b}=\frac{n}{c}$

the direction ratios of the bisectors of the angles between the two lines are $l \pm a, m \pm b$ and $n \pm c$

the direction ratios of the bisectors of the angles between the two lines are la, $m b$ and $n c$

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